关于UQR映射的无穷小空间
On the infinitesimal space of uqr mappings
摘要：
广义导数和无穷小空间将导数的概念推广到不需要是可微的映射。它在拟正则映射的情形下特别强大，其中正规族论证意味着广义导数总是存在。本文的主要结果是证明：若$f$是任何一致拟正则映射，且$x_0$是拓扑吸引或排斥的不动点，且$f$在该不动点处是局部内射的，则$f$可以共轭到具有不动点$0$的一致拟正则映射$g$，且使得$g$在$0$处的无穷小空间包含不可数个元素.这应该与$f$（以及$g$）在吸引或排斥情况下分别与$x\mapsto x/2$或$x\mapsto 2x$共轭的事实形成对比。
英文摘要：
Generalized derivatives and infinitesimal spaces generalize the idea of derivatives to mappings which need not be differentiable. It is particularly powerful in the context of quasiregular mappings, where normal family arguments imply generalized derivatives always exist. The main result of this paper is to show that if $f$ is any uniformly quasiregular mapping with $x_0$ a topologically attracting or repelling fixed point, at which $f$ is locally injective, then $f$ may be conjugated to a uniformly quasiregular mapping $g$ with fixed point $0$ and so that the infinitesimal space of $g$ at $0$ contains uncountably many elements. This should be contrasted with the fact that $f$ (and also $g$) is conjugate to $x\mapsto x/2$ or $x\mapsto 2x$ in the attracting or repelling cases respectively.
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